When you use apt to install a package, internally it uses dpkg. When you install a package using apt it first creates a list of all the dependencies and downloads it from the repository.

Once the download is finished it calls dpkg to install all those files, satisfying all the dependencies.

So if you have a .deb file:

You can install it using sudo dpkg -i /path/to/deb/file followed by sudo apt-get install -f.
You can install it using apt-get install package_name. But first move your deb file to /var/cache/apt/archives/ directory. After executing this command, it will automatically download its dependencies.

(it will work if the .deb package is present in the apt package list)

Install gdebi and open your .deb file using it (Right-click -> Open with). It will install your .deb package with all its dependencies.